Your point is well taken, LW. A counterpoint:

Yes, it was personal--how could his brother betraying him with near-lethal consequences not be personal?
But, Michael may have been coldly calculating, in addition to having the usual paranoia that comes with being a Don. He may have calculated that Fredo had been frightened enough by being found out so that he was not an immediate threat, especially since he wasn't living in the compound anymore, and was therefore not privy to info or proximity to Michael that could be useful to Michael's enemies. Another guess: Mama may have been sick, so his instruction to Neri--"I want nothing to happen to him as long as my mother is alive"--was a short term commitment. In the event, Mama died soon after: Michael returned from Cuba in 1959; the hearse outside Mama's wake is a '59 Cad, and Roth, who was whacked well after Mama died, said he was returning to the US to "vote in the [1960] election."

"Forgiving" Fredo at the wake, and allowing him to live in the compound, was the classic "keep your friends close but your enemies closer." Perhaps Michael, in his Donship paranoia, calculated that, after Mama died, Fredo would feel unconstrained to betray him again--just as, after Mama died, Michael felt unconstrained to whack Fredo.